2017/05/10 by Christian Mönch, Mönch, Christian
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1705.03801
openalex publication_date 2017/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a Poissonian model of directed random graphs which generalises the undirected Poissonian random graph process introduced by Norros and Reittu in Adv. Appl. Probab. 38 (2006), 59--75. Its loopless simple projection is a rank-one independent-arc inhomogeneous digraph of the type studied by Cao and Olvera-Cravioto, Random Struct. Alg. 56 (2020), 722--774. For the Poissonian multigraph itself, we discuss the relation to Norros-Reittu graphs, characterise limiting degree distributions, and record explicit exploration estimates. In particular, we give fixed-depth directed local weak limits, stopped branching-process couplings with weight-mass collision budgets, a comparison with the simple projection, and a rare-event concentration criterion. These estimates are intended as graph-side structural inputs for later dynamics on the graph.